Apparatus and method for determination of free fluid in subsurface formations

ABSTRACT

The disclosure is directed to an apparatus and method for determining the bound-water-filled porosity of formations surrounding a borehole. Bound-water-filled porosity is the fraction of the formation unit volume (matrix plus fluid) which is occupied by bound water, bound water being the portion of the total water which is adsorbed or bound to, or impermeably held by, the matrix. In one embodiment, means are provided for deriving a first quantity which is a measure of the attenuation of microwave electromagnetic energy passed through the formations of interest. This first quantity may be, for example, the attenuation constant determined for the microwave electromagnetic energy passing through the formations. Means are provided for generating a second quantity which is substantially proportional to the square of the first quantity. The second quantity is indicative of the bound-water-filled porosity of the formations. In another embodiment of the invention, means are provided for deriving a third quantity which is representative of the total porosity of the formations. In this embodiment, a further means is provided for generating a fourth quantity as a function of the difference between the third quantity and the second quantity, the fourth quantity being indicative of the free fluid index of the formations.

BACKGROUND OF THE INVENTION

This invention relates to the investigation of earth formations and,more particularly, to an apparatus and method for determining thebound-water-filled porosity of formations surrounding a borehole.

Modern well logging technology has advanced to a point where a number ofsubsurface parameters, for example porosity and lithology, can often bedetermined with reasonable accuracy. However, a reliable technique fordetermining the permeability of formations (i.e., a measure of the easewith which fluid can flow through a pore system), has not beenforthcoming. Resistivity gradients have been used to estimate the orderof magnitude of formation permeability, but this technique is founduseful only in certain types of formations. It has been suggested that ameasurement of the amount of "free fluid" in shaly formations would be agood permeability indicator. A known technique for measuring "freefluid" is the nuclear magnetic resonance tool, but attainablesignal-to-noise ratios tend to be a limiting factor of performance forthis tool.

In the copending U.S. patent application Ser. No. 674,791, now U.S. Pat.No. 4,063,151, of R. Rau and J. Suau, assigned to the same assignee asthe present application, there is disclosed a technique for determiningthe amount of bound water in formations surrounding a borehole bymeasuring the dielectric constant of the formations at two differentmicrowave frequencies. The difference between the measurements taken atthe two frequencies is utilized to determine the amount of bound waterin the formations. In another copending U.S. patent application Ser. No.674,792, now U.S. Pat. No. 4,077,003, of R. Rau, also assigned to thepresent assignee, determinations of dielectric loss factors are taken attwo different frequencies and are utilized to obtain information aboutthe amount of bound water in the formations.

It is one object of the present invention to determine, without the needfor dual frequency measurements, the bound-water-filled porosity offormations surrounding a borehole.

SUMMARY OF THE INVENTION

Applicant has discovered that the bound-water-filled porosity offormations surrounding a borehole can be determined from a measure ofthe attenuation of microwave electromagnetic energy, at a frequencywithin a predetermined range, passed through the formations of interest.In particular, over a range of frequencies from about 0.9 GHz to about1.3 GHz, and preferably at about 1.1 GHz, the bound-water-filledporosity is substantially proportional to the square of the measuredattenuation constant for the microwave electromagnetic energy passedthrough the formations of interest. The stated relationship is found tosubstantially apply even in the presence of a significant volume ofunbound ("free") water, typically mud filtrate (preferably of relativelyfresh mud) which has replaced movable fluids flushed from the invadedzone of the formations.

The present invention is directed to an apparatus and method fordetermining the bound-water-filled porosity of formations surrounding aborehole. As used herein, bound-water-filled porosity is intended tomean the fraction of the formation unit volume (matrix plus fluid) whichis occupied by bound water, bound water being that portion of the totalwater which is adsorbed or bound to, or impermeably held by, the matrix.Shales generally contain bound water and terms such as "shale water" arealso sometimes utilized to designate bound water. In accordance with anembodiment of the invention, means are provided for deriving a firstquantity which is a measure of the attenuation of microwaveelectromagnetic energy passed through the formations of interest. Thisfirst quantity may be, for example, the attenuation constant determinedfor the microwave electromagnetic energy passing through the formations.Means are provided for generating a second quantity which issubstantially proportional to the square of the first quantity. Thesecond quantity is indicative of the bound-water-filled porosity of theformations.

In another embodiment of the invention, means are provided for derivinga third quantity which is representative of the total porosity of theformations. The third quantity may be derived, for example, from otherlogging information. In this embodiment, a further means is provided forgenerating a fourth quantity as a function of the difference between thethird quantity and the second quantity, the fourth quantity beingindicative of the free fluid index of the formations.

Further features and advantages of the invention will become morereadily apparent from the following detailed description when taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation, partially in block form, of anapparatus incorporating an embodiment of the invention.

FIG. 2 illustrates, in simplified form, the nature of propagation of amicrowave electromagnetic lateral wave in the formations.

FIG. 3 is a block diagram of the amplitude comparator of FIG. 1.

FIG. 4 is a block diagram of the computing module of FIG. 1.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Consider a plane electromagnetic wave propagating in a lossy medium. Thepropagation constant, γ, of the wave is generally represented as

    γ=ω√με√1+j(σ/με(1)

where ω is the angular frequency of the wave, μ is the magneticpermeability of the medium, ε is the dielectric constant of the medium,and σ is the conductivity of the medium. It is conventional to expressthe real and imaginary parts of the propagation constant as β and α,respectively, so that

    γ=β+jα                                    (2)

where β is a phase constant and α is the attenuation constant of thewave. (Note that the propagation constant is used in the well known waveequation in the form e^(j)γ, so the real part of the propagationconstant becomes the imaginary part of the exponent, and vice versa.This accounts for the imaginary part of the propagation constant beingassociated with loss.) Squaring equations (1) and (2) and equating thereal and imaginary parts gives

    β.sup.2 -α.sup.2 =μεω.sup.2    (3)

and

    2αβ=μσω                          (4)

In the above referenced copending applications and in the U.S. Pat. No.3,944,910 there are disclosed techniques for determining the phase andattenuation constants associated with microwave electromagnetic energytraversing subsurface formations. The determined phase and/orattenuation information is then utilized, for example employing therelationships (3) and (4), to determine properties of the formations,such as its dielectric constant or its porosity. As noted in thebackground hereof, measurements taken at two different frequencies canalso be utilized to determine the amount of bound water in theformations. In the present invention the bound-water-filled porosity offormations, designated φ_(wb), is determined as being substantiallyproportional to the square of the measured attenuation constant for themicrowave electromagnetic energy passed through the formations. Inequation form, this is expressed by

    φ.sub.wb =Kα.sup.2                               (5)

the free fluid index ("FFI") is the fraction of the formation unitvolume occupied by "free" (unbound) fluid, that is

    FFI=φ.sub.t -φ.sub.wb                              (6)

where φ_(t) is total porosity of the formation.

Referring to FIG. 1, there is shown a representative embodiment of anapparatus in accordance with the present invention for investigatingsubsurface formations 31 traversed by a borehole 32. The borehole 32 istypically filled with a drilling fluid or mud which contains finelydivided solids in suspension. The investigating apparatus or loggingdevice 30 is suspended in the borehole 32 on an armored cable 33, thelength of which substantially determines the relative depth of thedevice 30. The cable length is controlled by suitable means at thesurface such as a drum and winch mechanism (not shown).

The logging device 30 includes an elongated cylindrical support member34, the interior portion of which has a fluid-tight housing containingthe bulk of the downhole electronics. Mounted on support member 34 are apair of bowed springs 35 and 36. The spring 35 has mounted thereon a padmember 37 which contains, inter alia, a transmitting antenna T andvertically spaced receiving antennas R₁ and R₂. Mounted on the spring 36is a secondary pad member 38 which may be an inactive pad thatfacilitates smooth vertical movement of the device 30 through theborehole. If desired, however, the pad 38 may contain electrodes or likeadditional means for investigating the surrounding formations.Electronic signals indicative of the in formation obtained by thelogging device are transmitted through the cable 32 to a computingmodule 85 and recorder 95 located at the surface of the earth. Theparticular means shown in FIG. 1 for maintaining the antennas inengagement with the borehole wall is illustrative, and it will beappreciated that other suitable means for accomplishing this objective,such as hydraulic means, can be utilized.

FIG. 2 illustrates, in simplified form, the nature of propagation of theelectromagnetic wave to be measured with the apparatus of FIG. 1. (For amore detailed description of the wave propagation path, as well asfurther description of the type of logging device employed herein andknown as an electromagnetic propagation tool or "EPT," reference can bemade to the U.S. Pat. No. 3,944,910 of R, Rau.) In FIG. 2 the pad 37 isshown positioned against the side of the borehole 32 which, asabove-stated, is filled with a drilling mud. Generally, the fluidpressure in the formations traversed by a borehole is less than thehydrostatic pressure of the column of mud in the borehole, so that themud and mud filtrate flows somewhat into the formations. The formationstend to screen the small particles suspended in the mud so that amudcake is formed on the walls of the borehole. The thickness of themudcake varies with formation parameters such as permeability, but atleast a very thin mudcake is usually present on the borehole wall. InFIG. 2, the pad 37 contacts a mudcake 40 which is shown as being ofexaggerated scole thickness for illustrative clarity.

The transmitting antenna T emits microwave electromagnetic energy intothe formation as represented by the arrow A. A resultant surface wavepropagating in the formation is represented by the arrow B and itsextension, arrow C. The surface wave continuously sheds energy back intothe more lossy media (the mudcake), and the portions of energy which areshed at the approximate locations of the receivers R₁ and R₂ arerepresented by the arrows D and E, respectively. If the pathlengthsrepresented by arrows D and E are assumed to be substantially equal, itis seen that the difference in pathlength between the energy received atR₁ (via path A-B-D) and the energy received at R₂ (via path A-B-C-E) isthe distance represented by arrow C; i.e., the distance between thereceivers. Accordingly, a differential receiver arrangement allowsinvestigation of the portion of the formation lying approximatelyopposite the separation between R₁ and R₂. Typically, but notnecessarily, the investigated formation will be the "flushed" or"invaded" zone which surrounds the mudcake in the borehole and containsfluids from the mud which filter through the mudcake. The EPT type ofdevice employed herein is particularly effective for investigating theinvaded zone in a borehole drilled with relatively fresh water-basedmud.

Referring again to FIG. 1, the downhole electronics contained within themember 34 are shown, for convenience of illustration, at the side of theborehole. A solid state oscillator 45 provides output energy in themicrowave region of the spectrum. The microwave region is defined hereinas including the range of frequencies between about 300 MHz and 300 GHz.The oscillator 45 may operate at the suitable frequency of 1.1 GHz; i.e.1.1×10⁹ cycles per second. The output of oscillator 45 is coupledthrough an isolator 46 to the transmitting antenna T. Microwave energyis transmitted into the surrounding formations and propagates throughthe formations in the manner previously described. The energy whicharrives at the receiving antennas R₁ and R₂ is respectively coupled toinput terminals of the mixers 47 and 48. The signals which arrive fromR₁ and R₂ are out of phase with each other by an amount which depends onthe phase constant β and have an amplitude ratio which depends upon theattenuation constant α. Secondary input terminals of the mixers aresupplied with microwave energy at a frequency that is separated from thetransmitter frequency by some relatively low frequency which istypically in the radio frequency range. In the embodiment shown, a solidstate oscillator 49 supplies microwave energy to mixers 47 and 48 at afrequency of 1.1001 GHz, or 100 KHz above the transmitter frequency. Theoutput signals 47A and 48A of the mixers 47 and 48 therefore contain thedifference frequency of 100 KC. In accordance with well knownprinciples, the signals 47A and 48A maintain the phase and amplituderelationships of the signals from R₁ and R₂, but the task of phasedetection (performed generally in this type of logging device, but notnecessary for the present invention) is greatly facilitated at the lowerfrequency of the mixed signals. To insure that the difference frequencybetween the outputs of the oscillators 45 and 49 remains at 100 KHz, theoscillator outputs are sampled and fed to a mixer 50. The output of themixer is received by a frequency stabilization circuit 51 which detectsdrifts from the 100 KHz standard and generates a correction signal 51Awhich controls oscillator 49 in the manner of a conventional"phase-locked loop."

The signals 47A and 48A are typically applied to a phase detectorcircuit (not required herein, and not shown) and to an amplitudecomparator 54. The output of amplitude comparator 54 is a signal levelwhich is proportional to the attenuation constant α. A convenientcircuit 54 for obtaining an output signal proportional to α is shown inFIG. 3. The signals 47A and 48A are respectively applied to thelogarithmic amplifiers 55 and 56 whose outputs are fed to the differenceamplifier 57. The output of the difference amplifier 57 is a signallevel proportional to α. This can be visualized by representing theamplitude of the wave energy received at R₁ as Ae⁻αz, where A is anamplitude constant and z is the distance separating T and R₁. It followsthat the amplitude of the wave energy received at R₂ is Ae⁻α(z+L), whereL is the distance separating the receivers R₁ and R₂. The ratio of thewave amplitudes at the two receivers is therefore

    Ae.sup.-α(z+L) /Ae.sup.-αz =e.sup.-αL.

the log of the ratio of the wave amplitudes is therefore proportional toα. It will be appreciated that the circuit 54 of FIG. 3 accomplishes thesame mathematical result by taking the difference of the logs of thewave amplitudes.

The output representative of α is transmitted to the surface over aconductor 54a which in actuality passes through the armored cable 33.Typically, the signal may be a DC level which is stepped up byamplification before transmission to the surface. At the surface of theearth the signal on line 54a is applied to a computing module 85 whichcomputes the bound-water-filled porosity, φ_(wb), of the formations inaccordance with the relationship (5). A signal representative of thetotal porosity, φ_(t), may also be input to the computing module 85which can then determine the free fluid index (FFI) of the formations inaccordance with the relationship (6). The computed quantities arerecorded by a recorder 95 that is conventionally driven as a function ofborehole depth by mechanical coupling to a rotating wheel 96. The wheel96 is coupled to the cable 33 and rotates in synchronism therewith so asto move as a function of borehole depth. Thus, the bound-water-filledporosity and/or the free fluid index of the formations are recorded as afunction of borehole depth by the recorder 95.

FIG. 4 is a block diagram of the computing module 85 which receives thesignal on line 54a that is indicative of the measured value of α. Thesignal representative of α is coupled to a squaring circuit 91, theoutput of which is representative of α². This signal is, in turn,applied to one input of a multiplier 92, the other input of whichreceives an adjustable input having a value designated K. Accordingly,the output of the multiplier 92 is a signal having a value Kα² and whichis representative of the bound-water-filled porosity, φ_(wb), of theformations, in accordance with the relationship (5). The output ofmultiplier 92 (line 85A) is coupled to the recorder 95 and also to thenegative input terminal of a difference amplifier 93. The positive inputterminal of the difference amplifier 93 receives a signal representativeof the total porosity of the formations of interest, φ_(t). This lattersignal may be determined, for example, from other logging information,such as from neutron/density logging information. The output ofdifference amplifier 93 (line 85B), also coupled to recorder 95, isrepresentative of the free fluid index of the formations, in accordancewith the relationship (6). As used herein, the bound-water-filledporosity and free fluid index are defined in terms of fractions of theformation total or bulk unit volume. In this sense, these terms areinterchangeable with similar terms expressing the amount, volume, orfraction of bound or free fluid in the formations.

The invention has been described with reference to a particularembodiment, but variations within the spirit and scope of the inventionwill occur to those skilled in the art. For example, while circuitry hasbeen described for generating analog signals representative of thedesired quantities, it will be understood that a general purpose digitalcomputer could readily be programmed to implement the techniques as setforth herein. Also, it should be noted that the advantageous principlesof known borehole compensation techniques and/or of redundant processingchannels, such as are disclosed in U.S. Pat. No. 3,849,721, can beutilized, if desired, in conjunction with the present invention.Further, it will be understood that the measured values can, if desired,be corrected for mudcake effect, spreading, or temperature variations,as is known in the art. Finally, although the illustrative embodimentshows various quantities as being derived directly from a loggingdevice, these quantities may alternatively be derived from storage mediaor communicated from a logging location.

I claim:
 1. Apparatus for determining the free fluid index of formationssurrounding a borehole, comprising:means for deriving a first quantitywhich is a measure of the attenuation of microwave electromagneticenergy passed through said formations; means for generating a secondquantity which is substantially proportional to the square of said firstquantity; means for deriving a third quantity which is a representativeof the total porosity of the formations; and means for generating afourth quantity as a function of the difference between said thirdquantity and said second quantity; said fourth quantity being indicativeof the free fluid index of said formations.
 2. Apparatus as defined byclaim 1 wherein said first quantity is the attenuation constant ofmicrowave electromagnetic energy passed through the formations. 3.Apparatus as defined by claim 1 wherein said microwave electromagneticenergy has a frequency of about 1.1 GHz.
 4. Apparatus as defined byclaim 1 wherein said microwave electromagnetic energy has a frequency ofabout 1.1 GHz.
 5. Apparatus for determining the free fluid index offormations surrounding a borehole, comprising:means for injectingmicrowave electromagnetic energy into the formations; means formeasuring the attenuation of the microwave electromagnetic energypassing through the formations; means responsive to the measuredattenuation for generating a signal which is substantially proportionalto the square of the measured attenuation; means for deriving anothersignal which is representative of the total porosity of the formations;and means for generating a further signal as a function of thedifference between said another signal and said signal; said furthersignal being indicative of the free fluid index of said formations. 6.Apparatus as defined by claim 5 wherein said means for measuringattenuation includes means for obtaining the attenuation constant ofsaid formations.
 7. Apparatus as defined by claim 5 wherein saidmicrowave electromagnetic energy has a frequency of about 1.1 GHz. 8.Apparatus as defined by claim 6 wherein said microwave electromagneticenergy has a frequency of about 1.1 GHz.
 9. A method for determining thefree fluid index of formations surrounding a borehole, comprising thesteps of:deriving a first quantity which is a measure of the attenuationof microwave electromagnetic energy passed through said formations;generating a second quantity which is substantially proportional to thesquare of said first quantity; deriving a third quantity which is ameasure of the total porosity of the formations; and generating a fourthquantity as a function of the difference between said third quantity andsaid second quantity; said fourth quantity being indicative of the freefluid index of said formations.
 10. The method as defined by claim 9wherein said first quantity is the attenuation constant of microwaveelectromagnetic energy passed through the formations.
 11. The method asdefined by claim 9 wherein said microwave electromagnetic energy has afrequency of about 1.1 GHz.
 12. The method as defined by claim 10wherein said microwave electromagnetic energy has a frequency of about1.1 GHz.
 13. A method for determining the bound-water-filled porosity offormations surrounding a borehole, comprising the steps of:injectingmicrowave electromagnetic energy into the formations; measuring theattenuation of the microwave electromagnetic energy passing through theformations; generating a signal which is substantially proportional tothe square of the measured attenuation; deriving another signal which isrepresentative of the total porosity of the formations; and generating afurther signal as a function of the difference between said anothersignal and said signal; said further signal being indicative of the freefluid index of said formations.
 14. The method as defined by claim 13wherein the step of measuring attenuation includes determining theattenuation constant of said formations.
 15. The method as defined byclaim 13 wherein said microwave electromagnetic energy has a frequencyof about 1.1 GHz.
 16. The method as defined by claim 14 wherein saidmicrowave electromagnetic energy has a frequency of about 1.1 GHz.